A passively Q-switched tunable Yb-doped double-clad fiber laser is demonstrated with graphene epitaxially grown on SiC. The spectral tuning of the Q-switched fiber laser is implemented by rotating a quartz plate filter inside the cavity. The central wavelength of the fiber laser can be continuously tuned from 1038.54 to 1056.22 nm. The maximum pulse energy of 0.65 \mu J is obtained at the pump power of 4.08 W, and the corresponding pulse duration and average output power are 1.60 \mu s and 35 mW, respectively.